The Steepest Descent Algorithm for Unconstrained ...
If x =¯x is a given point, f(x) can be approxi-mated by its linear expansion f(¯x+ d) ≈ f(¯x)+∇f(¯x)T d if d “small”, i.e., if d is small. Now notice that if the approximation in the above expression is good, then we want to choose d so that the inner product ∇f(¯x)T d is as small as possible. Let us normalize d so that d =1.
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